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Even as Donald Trump readies to take the oath of office, his Cabinet picks face a rough week in the Capitol

Selections for Health and Human Services, the Treasury Department and Labor are all under attack

Washington (CNN)Even as Donald Trump readies to take the oath of office on the west side of the Capitol, some of his top Cabinet picks are off to a rocky start this week inside the building, facing surprising heat.

Senate Minority Leader Chuck Schumer opened Inauguration Week Tuesday morning by saying that Trump's pick to oversee the dismantling of Obamacare, Tom Price, may have broken the law with a stock purchase last year and should be investigated.

Meanwhile, questions have swirled about how prepared (and willing) Trump's picks for the Treasury and Labor departments are to face a barrage of criticism at their hearings. And another top Trump aide split after CNN uncovered examples of her plagiarizing multiple works.

Tom Price, a former top Republican in the House and medical doctor is set for a hearings before a pair of Senate committees before he can take the helm at the Department of Health and Human Services. And those hearings promise to be painful after reports that Price may have tried to help companies that he bought stock in.

CNN broke the news Monday that Price bought up to $15,000 in stock in a medical device company, Zimmer Biomet, one month before introducing legislation that could have helped the stock's value go up. A Price aide later explained that Price was unaware of the purchase at the time because it was made by his broker.

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"If he knew about it, it could very well be a violation of the law," Schumer later told CNN's Manu Raju. "Now they say there's a broker, it's kind of strange that this broker would pick this stock totally independently of him introducing legislation that's so narrow and specific to this company."

It's a particularly auspicious time for the incoming Trump administration as it tries to find its footing on the chief issue absorbing all of Washington: replacing Obamacare. And Price is set to be at the forefront of that drive.

Then, a week later, Crowley bowed out. There have been other high-profile aides who departed before Trump took office, including Jason Miller, Crowley's plagiarism became a magnet for continued stories and criticism.

Trump's promise to bring outsiders into his Cabinet -- which has often resulted in billionaires taking on major roles -- has turned confirmation hearings in Capitol into a shooting gallery with Trump's top aides unable to dodge the fire, from Democrats and even some Republicans.

Reports surfaced at the start of the week that Trump's labor pick, fast food CEO Andy Puzder, had been voicing second thoughts about going before the firing squad -- although Puzder later said he was ready for his hearing.

Meanwhile, Axios' Mike Allen reported that additional aides had to be brought in for former Goldman Sachs partner Steven Mnuchin, after he came off as "uneven and stiff" in his early prep sessions.